Related papers: Least square estimators in linear regression model…
This paper deals with subspace estimation in the small sample size regime, where the number of samples is comparable in magnitude with the observation dimension. The traditional estimators, mostly based on the sample correlation matrix, are…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…
We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…
In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We study the performance of the Least Squares Estimator (LSE) in a general nonparametric regression model, when the errors are independent of the covariates but may only have a $p$-th moment ($p\geq 1$). In such a heavy-tailed regression…
We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in…
Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…
This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations…
Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
The paper continues the authors' work on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper it is shown that if the mean response function satisfies a condition of `saturated identifiability', which was…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.)…
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under…